Abstract

Based on a focusing Mikaelian’s lens with small refraction index (0<n<<1), an optical device is designed as a super-thin optical beam compressor (e.g., thickness = 3λ0) with an extremely high beam compression ratio (more than 19:1). This device can also be used as a beam collimator or a cylindrical-to-plane wave convertor with a much higher transmissivity than a zero-index metamaterial slab. The output beam shows good directionality in both near field and far field. A metamaterial structure is also designed to realize this device and verify its performance with finite element method (FEM).

© 2013 OSA

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    [CrossRef] [PubMed]
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2011 (1)

D. V. Nesterenko, “Metal-dielectric Mikaelian’s lens,” Computer Optics35(1), 47 (2011) (in Russian; not accessible to the authors, but mentioned by a reviewer).

2010 (4)

2009 (3)

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett.102(13), 133902 (2009).
[CrossRef] [PubMed]

M. I. Kotlyar, Y. R. Triandaphilov, A. A. Kovalev, V. A. Soifer, M. V. Kotlyar, and L. O’Faolain, “Photonic crystal lens for coupling two waveguides,” Appl. Opt.48(19), 3722–3730 (2009).
[CrossRef] [PubMed]

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys.5(9), 687–692 (2009).
[CrossRef]

2008 (6)

H. Ma, S. Qu, Z. Xu, and J. Wang, “Using photon funnels based on metamaterial cloaks to compress electromagnetic wave beams,” Appl. Opt.47(23), 4193–4195 (2008).
[CrossRef] [PubMed]

J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett.101(20), 203901 (2008).
[CrossRef] [PubMed]

Y. R. Triandaphilov and V. V. Kotlyar, “Photonic crystal Mikaelian lens,” Opt. Mem. Neural. Networks17(1), 1–7 (2008).

H. Ma, S. Qu, Z. Xu, and J. Wang, “General method for designing wave shape transformers,” Opt. Express16(26), 22072–22082 (2008).
[CrossRef] [PubMed]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett.100(6), 063903 (2008).
[CrossRef] [PubMed]

Y. Jin and S. L. He, “Impedance-matched multilayered structure containing a zero-permittivity material for spatial filtering,” J. Nonlinear Opt. Phys. Mater.17(03), 349–355 (2008).
[CrossRef]

2007 (2)

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.76(2), 026606 (2007).
[CrossRef] [PubMed]

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

2006 (3)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys.8(10), 247 (2006).
[CrossRef]

2005 (1)

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(33 Pt 2B), 036609 (2005).
[CrossRef] [PubMed]

2004 (2)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004).
[CrossRef] [PubMed]

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(4), 046608 (2004).
[CrossRef] [PubMed]

2000 (2)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

R. Ilinsky, “Gradient-index meniscus lens free of spherical aberration,” J. Opt. A, Pure Appl. Opt.2(5), 449–451 (2000).
[CrossRef]

1980 (1)

A.L. Mikaelian, “Self-focusing medium with variable index of refraction,” in Progress in Optics XVII, 283–346 (1980).

1952 (1)

A. L. Mikaelian, “General method of inhomogeneous media calculation by the given ray traces,” Dokl. Akad. Nauk83(2), 219 (1952).

1951 (1)

A. L. Mikaelian, “Application of stratified medium for waves focusing,” Dokl. Akad. Nauk SSSR81, 569–571 (1951).

Alù, A.

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

Cabrini, S.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett.102(13), 133902 (2009).
[CrossRef] [PubMed]

Chang, A. S. P.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett.102(13), 133902 (2009).
[CrossRef] [PubMed]

Cui, T. J.

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.76(2), 026606 (2007).
[CrossRef] [PubMed]

Cummer, S. A.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett.100(6), 063903 (2008).
[CrossRef] [PubMed]

Dardano, P.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett.102(13), 133902 (2009).
[CrossRef] [PubMed]

Dhuey, S.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett.102(13), 133902 (2009).
[CrossRef] [PubMed]

Engheta, N.

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

Genov, D. A.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys.5(9), 687–692 (2009).
[CrossRef]

Hao, Y.

Harteneck, B.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett.102(13), 133902 (2009).
[CrossRef] [PubMed]

He, S.

He, S. L.

Y. Jin and S. L. He, “Impedance-matched multilayered structure containing a zero-permittivity material for spatial filtering,” J. Nonlinear Opt. Phys. Mater.17(03), 349–355 (2008).
[CrossRef]

Huang, D.

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.76(2), 026606 (2007).
[CrossRef] [PubMed]

Ilinsky, R.

R. Ilinsky, “Gradient-index meniscus lens free of spherical aberration,” J. Opt. A, Pure Appl. Opt.2(5), 449–451 (2000).
[CrossRef]

Jiang, Z. H.

Jin, Y.

Y. Jin and S. He, “Enhancing and suppressing radiation with some permeability-near-zero structures,” Opt. Express18(16), 16587–16593 (2010).
[CrossRef] [PubMed]

Y. Jin and S. L. He, “Impedance-matched multilayered structure containing a zero-permittivity material for spatial filtering,” J. Nonlinear Opt. Phys. Mater.17(03), 349–355 (2008).
[CrossRef]

Kotlyar, M. I.

Kotlyar, M. V.

Kotlyar, V. V.

V. V. Kotlyar, A. A. Kovalev, and V. A. Soifer, “Subwavelength focusing with a Mikaelian planar lens,” Opt. Mem. Neural. Networks19(4), 273–278 (2010).
[CrossRef]

Y. R. Triandaphilov and V. V. Kotlyar, “Photonic crystal Mikaelian lens,” Opt. Mem. Neural. Networks17(1), 1–7 (2008).

Kovalev, A. A.

V. V. Kotlyar, A. A. Kovalev, and V. A. Soifer, “Subwavelength focusing with a Mikaelian planar lens,” Opt. Mem. Neural. Networks19(4), 273–278 (2010).
[CrossRef]

M. I. Kotlyar, Y. R. Triandaphilov, A. A. Kovalev, V. A. Soifer, M. V. Kotlyar, and L. O’Faolain, “Photonic crystal lens for coupling two waveguides,” Appl. Opt.48(19), 3722–3730 (2009).
[CrossRef] [PubMed]

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006).
[CrossRef] [PubMed]

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys.8(10), 247 (2006).
[CrossRef]

Li, J.

J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett.101(20), 203901 (2008).
[CrossRef] [PubMed]

Liu, R.

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.76(2), 026606 (2007).
[CrossRef] [PubMed]

Ma, H.

Massoud, A. T.

Medina, F.

Mikaelian, A. L.

A. L. Mikaelian, “General method of inhomogeneous media calculation by the given ray traces,” Dokl. Akad. Nauk83(2), 219 (1952).

A. L. Mikaelian, “Application of stratified medium for waves focusing,” Dokl. Akad. Nauk SSSR81, 569–571 (1951).

Mikaelian, A.L.

A.L. Mikaelian, “Self-focusing medium with variable index of refraction,” in Progress in Optics XVII, 283–346 (1980).

Mocella, V.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett.102(13), 133902 (2009).
[CrossRef] [PubMed]

Mock, J. J.

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(33 Pt 2B), 036609 (2005).
[CrossRef] [PubMed]

Moretti, L.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett.102(13), 133902 (2009).
[CrossRef] [PubMed]

Nesterenko, D. V.

D. V. Nesterenko, “Metal-dielectric Mikaelian’s lens,” Computer Optics35(1), 47 (2011) (in Russian; not accessible to the authors, but mentioned by a reviewer).

O’Faolain, L.

Olynick, D.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett.102(13), 133902 (2009).
[CrossRef] [PubMed]

Pendry, J. B.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett.100(6), 063903 (2008).
[CrossRef] [PubMed]

J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett.101(20), 203901 (2008).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Philbin, T. G.

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys.8(10), 247 (2006).
[CrossRef]

Qu, S.

Rahm, M.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett.100(6), 063903 (2008).
[CrossRef] [PubMed]

Rendina, I.

V. Mocella, S. Cabrini, A. S. P. Chang, P. Dardano, L. Moretti, I. Rendina, D. Olynick, B. Harteneck, and S. Dhuey, “Self-collimation of light over millimeter-scale distance in a quasi-zero-average-index metamaterial,” Phys. Rev. Lett.102(13), 133902 (2009).
[CrossRef] [PubMed]

Salandrino, A.

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

Schurig, D.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett.100(6), 063903 (2008).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(33 Pt 2B), 036609 (2005).
[CrossRef] [PubMed]

Silveirinha, M.

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007).
[CrossRef]

Smith, D. R.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett.100(6), 063903 (2008).
[CrossRef] [PubMed]

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.76(2), 026606 (2007).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(33 Pt 2B), 036609 (2005).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004).
[CrossRef] [PubMed]

Soifer, V. A.

V. V. Kotlyar, A. A. Kovalev, and V. A. Soifer, “Subwavelength focusing with a Mikaelian planar lens,” Opt. Mem. Neural. Networks19(4), 273–278 (2010).
[CrossRef]

M. I. Kotlyar, Y. R. Triandaphilov, A. A. Kovalev, V. A. Soifer, M. V. Kotlyar, and L. O’Faolain, “Photonic crystal lens for coupling two waveguides,” Appl. Opt.48(19), 3722–3730 (2009).
[CrossRef] [PubMed]

Starr, A. F.

D. R. Smith, J. J. Mock, A. F. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.71(33 Pt 2B), 036609 (2005).
[CrossRef] [PubMed]

Tang, W. X.

Triandaphilov, Y. R.

Turpin, J. P.

Wang, J.

Werner, D. H.

Werner, P. L.

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004).
[CrossRef] [PubMed]

Xu, Z.

Zhang, S.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys.5(9), 687–692 (2009).
[CrossRef]

Zhang, X.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys.5(9), 687–692 (2009).
[CrossRef]

Zhao, B.

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.76(2), 026606 (2007).
[CrossRef] [PubMed]

Ziolkowski, R. W.

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.70(4), 046608 (2004).
[CrossRef] [PubMed]

Appl. Opt. (2)

Computer Optics (1)

D. V. Nesterenko, “Metal-dielectric Mikaelian’s lens,” Computer Optics35(1), 47 (2011) (in Russian; not accessible to the authors, but mentioned by a reviewer).

Dokl. Akad. Nauk (1)

A. L. Mikaelian, “General method of inhomogeneous media calculation by the given ray traces,” Dokl. Akad. Nauk83(2), 219 (1952).

Dokl. Akad. Nauk SSSR (1)

A. L. Mikaelian, “Application of stratified medium for waves focusing,” Dokl. Akad. Nauk SSSR81, 569–571 (1951).

J. Nonlinear Opt. Phys. Mater. (1)

Y. Jin and S. L. He, “Impedance-matched multilayered structure containing a zero-permittivity material for spatial filtering,” J. Nonlinear Opt. Phys. Mater.17(03), 349–355 (2008).
[CrossRef]

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Nat. Phys. (1)

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New J. Phys. (1)

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[CrossRef]

Opt. Express (4)

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[CrossRef]

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Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (3)

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Figures (8)

Fig. 1
Fig. 1

The 2D TE polarization FEM simulation result. The thickness of the ML is d = π/2g = 6λ0 and the height is h = 16λ0. The incident wave is a Gauss beam with waist radius w = 5λ0. The absolute value of electric fields in z direction are shown with (a) n0 = 1, (b) n0 = 0.6, (c) n0 = 0.2 and (d) n0 = 0.1. In order to show clearly the output beam, we rescale the color bar. The white regions mean the amplitude of the electric field is larger than the maximum value in the color bar.

Fig. 2
Fig. 2

The 2D FEM simulation result (TE polarization) when we set a line current with distance λ0 away from the front surface of an ML or a zero-index slab for (a), (b) and (c). We only plot the absolute value of the electric field after the slab. (a) The ML’s case with thickness d = π/2g = 6λ0, height h = 16λ0 and n0 = 0.2. (b) A zero-refraction index slab with thickness d = 6λ0, height h = 16λ0. (c) The ML’s case with thickness d = π/2g = 6λ0, height h = 16λ0 and n0 = 3. (d) The 2D FDTD simulation result (TE polarization) for the amplitude of the electric field. Both the structure and the incident wave in this simulation are the same as those for Fig. 1(c). The FDTD simulation is based on Meep (http://ab-initio.mit.edu/wiki/index.php/Meep).

Fig. 3
Fig. 3

(a) The four regions of the proposed device. (b) the refraction index distribution of this new device based on ML’s refraction index profile. The white regions in (a) and (b) represent the free space. When we set a line current at the center of the device, the absolute value of the electric field distribution outside the device is shown in (c) and (d) (calculated with FEM simulation for the 2D TE polarization case). (c) The device with refraction index profile in (b). (d) The four regions of the device are filled with a zero-index material. The white regions in (c) and (d) are where the amplitude of the electric field is larger than the maximum value in the color bar.

Fig. 4
Fig. 4

FEM simulation results (for TE polarization) when the incident wave is a plane wave with unit amplitude for a 2D ML with n0 = 0.2 [(a), (b) and (c)], and for a beam compressor designed by TO [(d) and (e)]. All devices have the same thickness d = 3λ0, height h = 90λ0 and a compression ratio of 19:1. (a) Distribution of the absolute value of the electric field in the ML with transmissivity 7.15%. The white regions are where the amplitude of electric field is larger than the maximum value in the color bar. (b) The normalized absolute value of the output beam from the ML in far field which shows a good directionality of the output beam. (c) The absolute value of the electric field in the impedance matched ML with ε = μ = n0sech(gy) with transmissivity 99.12%. (d) Distribution of the absolute value of electric field behind the TO-based compressor. (e) Far field pattern of the output beam from the TO-based device. The compression ratio is defined as the full width of null-to-null magnitude (FWNM) of the incident beam to the FWNM of the output beam. (f) A plane wave with full width 90λ0 incident on a diaphragm with a hole width 4.77λ0 (equivalent to the full width of the output beam in (a)).

Fig. 5
Fig. 5

The 2D FEM simulation results (for TE wave) when a plane wave impinges on an ML with n0 = 0.2. (a) The relation between the transmissivity and the thickness of an ML with fixed height h = 90λ0. (b) The relation between the size of the output beam and the size of the incident beam for an ML with fixed thickness d = 3λ0. One sees that the spot size of the output beam has a nearly constant FWHM around 3.4λ0. FWHM means the full width of half magnitude. (c) The relation between the size of the output beam (λ0 after the back surface of the ML with fixed height h = 90λ0) and the thickness of the ML. One sees that the spot size of the output beam has a nearly constant FWHM around 3.4λ0.

Fig. 6
Fig. 6

FEM simulation results (for TE polarization) when the incident wave is a plane wave with unit amplitude and full width 90λ0 incident on an ML with n0 = 0.2 n = n0*sech(gy), thickness d = 3λ0, height h = 90λ0 [(a) and (b)] and an impedance matched ML with n0 = 0.2 ε = μ = n0*sech(gy), thickness d = 3λ0, height h = 90λ0 [(c) and (d)]. We add a diaphragm with width 6λ0 before the ML in (b) and the impedance matched ML in (d). To illustrate whether the edge part of the incident beam really contributes to the output beam, we only plot the electric field amplitude of the output beam.

Fig. 7
Fig. 7

(a) A unit cell in the designed metamaterial: we set a cylindrical copper wire with diameter Dr and infinitely long in the z direction at the center of a square unit of 10 mm x10 mm. The square region is filled with air. (b) The diameter of each cylindrical copper wire and the effective refraction index of each metamaterial unit in different rows of the whole device. From the center y = 0 to two edges of the ML, we label rows 1 to 15.

Fig. 8
Fig. 8

The 2D FEM simulation results (for TE polarization) for the Mikaelian’s lens. The distribution of the absolute value of the electric field in the ML structure with the designed material parameters [(a) and (b)] and the reduced material parameters (c) with n0 = 0.3, thickness d = 3λ0 and height H = 10λ0. The input beam is a plane wave with width w = 5λ0 and a wavelength of λ0 = 30 mm (a), λ0 = 29 mm (b), and λ0 = 30 mm (c). Here we use the PEC (perfect electric conductor) model for the copper.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

n= n 0 sech(gr),
n= n 0 sech(gy).
λ| ¯ n|<<n,
λ 0 <<|1/sinh(gy)|,
x'=x,y'=(1/α1)xy/d+y,z'=z,
ε=μ= 1 a 22 [ 1 a 21 0 a 21 a 21 2 + a 22 2 0 0 0 1 ],
a 22 =1+( 1/α1 )x'/d,
a 21 =(1α)y'/[(1α)x'+αd].

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